Short answer: yes, but way less than you'd think.
Someone in a Discord I'm in claimed that Bluetooth controllers drain your phone twice as fast. That did not match my experience so I ran a very unscientific test.
One hour of Sideswipe, screen at 60% brightness, framerate capped at 60, on the same charge cycle both days.
Touch: phone dropped from 100% to 74%. So 26% for the hour.
Controller (Xbox pad over Bluetooth): 100% to 71%. 29% for the hour.
So yeah, controllers use more battery. Three percentage points more, roughly. That's the difference between 'my phone will last today' and 'my phone will last today.' It's basically nothing.
The real battery killer is the screen and the SoC when it's thermally throttling and boosting on and off. Cap your framerate, dim your screen, and you'll get way more play time whether you're on sticks or not.